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What do you think will be the role of the U.S.A. in the world where China may become the largest economy?

China's economic growth will taper off. The U.S. will retain world leadership both in politics and in economy.
China's economy will soon overtake that of the U.S., and the world governance will be the prerogative of the United Nations.
China's economy will soon overtake that of the U.S., but the U.S. will retain leadership in the world.
China's economic growth will taper off, but the U.S. will gradually 'retreat' from the role of the world police.
Others

Unexpectedly, Russia has emerged as a positive force in the eyes of the West. The eternal spoiler has turned into a benevolent power which toils to find a common solution with the West. This shows that the Russian government would be able to rally its people under a forward-looking banner, "Russia will build a better world as a member of the civilized global community," without resorting to a negative emotion such as xenophobia. This is the line for success at the Sochi Olympics and Sochi G8 summit meeting next year and for the ultimate accession of Russia to the Organization for Economic Cooperation and Development. By mending the relations with the United States Russia can also avoid an overdependence on China.

Probably, things in Syria will not proceed as smoothly as desired; there are forces which are eager to use the U.S. hitting power and to topple the Assad regime. The irresoluteness of the United States about the use of armed forces has generated anxiety among the U.S. allies; they wonder, "In case of emergency will the United States really come to help?" And such anxiety is augmented when they realize the general atmosphere in the United States where most people are against armed intervention abroad. The allies fear: perhaps, Syria's case is the precursor of the collapse of the U.S. alliance system.

However, the case is in fact totally different for the allies of the United States. In Japan and Western Europe the United States stations large armed forces at numerous military bases. An attack on any ally automatically incurs involvement of the U.S. armed forces. Moreover, the United States still to a significant extent depends on the oil imports from the Gulf States (about 15 percent of its total oil imports) with the tankers navigating through the Indian Ocean and the South China Sea and then further on to the United States. Safe and free navigation in these seas, therefore, is a sine qua non for the United States. This comes in handy for Japan and other Asian countries, because they are today confronting China in maritime territorial disputes. If any ally or quasi-ally unnecessarily provokes China, the United States may hesitate to intervene. But otherwise, the United States will continue to act as the guarantor of the status quo in the Western Pacific.

On Syria the United States and Russia have been able to churn a joint solution (short-lived, perhaps), because both parties limited the scope of negotiation only to the chemical weapons. Such global problems are easier to tackle. But when it comes to more fundamental questions such as "How to stop a civil war in a third country?" and "How to prevent collision between sovereign states?" the world is still in a rather hopeless situation.

The rivalry between Iran and Saudi Arabia lies in the background of the Syrian upheaval, but who can stop this vain contention and how? When the medieval feudal lords fought with each other, only weapons helped them--until the mightiest conquered them all and imposed law and order in the whole realm. The world has not changed in this regard; it still remains in a medieval order. We can only wish that countries be deprived of the weapons of mass destruction and that they abide by civilized norms when fighting--just like in Karate, bow first and then exterminate your opponent.